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Breaking prime to bust anchors..

Here is a situation that comes up now and again. You get lucky and hit 2 of your opponent last checkers. Now you are actually slightly the favorite. So you went from certain gammon death to a chance to win. There is however, a big difference between your opponent checkers both on the bar, or anchored in your home board. If you start bearing off while you have 2 checkers trapped on the bar, your chance of wining is high. If your opponent anchors on your home board, you have problems. You are bearing in against an anchor which gets awkward, and your opponent can roll doubles and scamper home before you get any checkers off. So you have to try hard not to allow the opponent to anchor. That means hitting loose and do what u have to do. So that is the first mistake I made in this game. I did not attack the blot on my home board, and my opponent anchored on the next roll, which gave this position
1.jpg
3 pt match, I am holding 2 cube, score 0-0

So what to do with this 3-2 roll ?
The best move is to force your opponent to break anchor.
All the top moves involve breaking your prime to force your opponent to move.
Once the opponent checkers are off the anchor and vulnerable to attack, you can hit hit hit and put both back on the bar.
Maintaining the prime and moving 12/7 turned out to be a .132 blunder.

1. Cubeful 3-ply 7/4 3/1 Eq.: +0.268
0.551 0.000 0.000 - 0.449 0.091 0.042

2. Cubeful 3-ply 7/5 4/1 Eq.: +0.252 ( -0.016)
0.545 0.000 0.000 - 0.455 0.094 0.047

3. Cubeful 3-ply 22/19 7/5 Eq.: +0.251 ( -0.017)
0.541 0.000 0.000 - 0.459 0.077 0.033

4. Cubeful 3-ply 22/20 7/4 Eq.: +0.242 ( -0.026)
0.537 0.000 0.000 - 0.463 0.077 0.031

5. Cubeful 3-ply 12/9 7/5 Eq.: +0.231 ( -0.037)
0.535 0.000 0.000 - 0.465 0.084 0.031

6. Cubeful 3-ply 12/7 Eq.: +0.136 ( -0.132)
0.497 0.000 0.000 - 0.503 0.088 0.021

So.. is breaking prime SCARY? :D Yes it is. Intuition is screaming NO, DON'T BREAK PRIME. But this is a special circumstance. Only 2 opponent checkers are left. The opponent home board is empty so there is no risk of getting stuck on the bar if hit. The opponent is happy to sit safe on that anchor while waiting for a chance to escape. We don't want to make life easy for the opponent. We must break up our prime, force the opponent to play a roll, attack attack attack, and put both those checkers back up on the bar where they belong :D
correct.jpg
Position after correct play of 3-2


1.jpg
Winning chance above 64%





2.jpg
Winning chance above 38%.
You don't want the last 2 anchored.
You want them on the bar.
Huge difference in the win rate between the positions. 64% vs 38%
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Re: Breaking prime to bust anchors..

Here is another similar position where a counter intuitive bold play is the best move. Anything else is losing lots of equity.
Can you guess what the correct play is?

7 pt match score 6-4 (red trailing, crawford)
Image
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admin
Site Admin
Posts: 353
Joined: Sun Oct 24, 2010 8:32 pm
Years playing backgammon: 20+ Learned to play on fibs.com playing bots and review with gnubg analysis FIBS rating 1750-1850
Location: USA

Re: Breaking prime to bust anchors..

1. Rollout 8/3 7/1 Eq.: +0.152

2. Rollout 16/11 7/1 Eq.: +0.046 (-0.105)

3. Rollout 16/10 8/3 Eq.: +0.040 (-0.112)

4. Rollout 16/10 6/1 Eq.: -0.039 (-0.191)

5. Rollout 16/5 Eq.: -0.053 (-0.205)

6. Rollout 7/1 6/1 Eq.: -0.065 (-0.216)
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